Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T02:38:05.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaporation-driven Contact Angles in a Pure-vapor Atmosphere :the Effect of Vapor Pressure Non-uniformity

Published online by Cambridge University Press:  09 July 2012

A.Y. Rednikov  and
P. Colinet
Get access

Abstract

A small vicinity of a contact line, with well-defined (micro)scales (henceforth the“microstructure”), is studied theoretically for a system of a perfectly wetting liquid,its pure vapor and a superheated flat substrate. At one end, the microstructure terminatesin a non-evaporating microfilm owing to the disjoining-pressure-induced Kelvin effect. Atthe other end, for motionless contact lines, it terminates in a constant film slope(apparent contact angle as seen on a larger scale), the angle being non-vanishing despitethe perfect wetting due to an overall dynamic situation engendered by evaporation. Here wego one step beyond the standard one-sided model by incorporating the effect of vaporpressure non-uniformity as caused by a locally intense evaporation flow, treated in theStokes approximation. Thereby, the film dynamics is primarily affected throughthermodynamics (shift of the local saturation temperature and evaporation rate), thedirect mechanical impact being rather negligible. The resulting integro-differentiallubrication film equation is solved by handling the newly introduced effect (giving riseto the “integro” part) as a perturbation. In the ammonia (at 300   K) example dealt withhere, it proves to be rather weak indeed: the contact angle decreases while the integralevaporation flux increases just by a few percent for a superheat of  ~1   K.However, the numbers grow (roughly linearly) with the superheat.

Keywords

contact angleevaporationsuperheatpure vaporthin filmsnonlocal effect
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 53 - 63
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ajaev, V.S.. Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech., 528 (2005), 279–296. CrossRefGoogle Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J., Rolley, E.. Wetting and spreading. Rev. Mod. Phys., 81 (2009), 739–805. CrossRefGoogle Scholar
Burelbach, J.P., Bankoff, S.G., Davis, S.H.. Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech., 195 (1988), 463–494. CrossRefGoogle Scholar
de Gennes, P.G.. Wetting : statics and dynamics. Rev. Mod. Phys., 57 (1985), 827–863. CrossRefGoogle Scholar
P.G. de Gennes, F. Brochard-Wyart, D. Quéré. Capillarity and wetting phenomena. Springer, 2004.
Moosman, S., Homsy, G.M.. Evaporating menisci of wetting fluids. J. Colloid Interface Sci., 73 (1980), 212–223. CrossRefGoogle Scholar
Morris, S.J.S.. Contact angles for evaporating liquids predicted and compared with existing experiments. J. Fluid Mech., 432 (2001), 1–30. Google Scholar
Oron, A., Davis, S.H., Bankoff, S.G.. Long-scale evolution of thin liquid films. Rev. Mod. Phys., 69 (1997), 931–980. CrossRefGoogle Scholar
Potash, M., Wayner, P.C.. Evaporation from a two dimensional extended meniscus. Int. J. Heat Mass Transfer, 15 (1972), 1851–1863. CrossRefGoogle Scholar
Rednikov, A.Ye., Colinet, P.. Vapor-liquid steady meniscus at a superheated wall : asymptotics in an intermediate zone near the contact line. Microgravity Sci. Tech., 22 (2010), 249–255. CrossRefGoogle Scholar
Rednikov, A.Ye., Rossomme, S., Colinet, P.. Steady microstructure of a contact line for a liquid on a heated surface overlaid with its pure vapor : parametric study for a classical model. Multiphase Sci. Tech., 21 (2009), 213–248. CrossRefGoogle Scholar
R.W. Schrage. A Theoretical Study of Interface Mass Transfer. Columbia University Press, New York, 1953.
Stephan, P.C., Busse, C.A.. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int. J. Heat Mass Transfer, 35 (1992), 383–391. CrossRefGoogle Scholar